Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and numerical approaches demonstrate that linear stability requires boundedness of propagation speeds of normal eigen-modes. The study provides a basis for the construction of unconditionally stable lattice Boltzmann models.

翻译：本文针对一类具有非理想状态方程的格子玻尔兹曼模型，详细研究了其谱特性与线性稳定性。研究实例包括范德瓦尔斯模型与浅水模型。解析与数值方法均表明，线性稳定性要求法向本征模的传播速度有界。本研究为构建无条件稳定的格子玻尔兹曼模型提供了理论基础。